A conserved quantity in thin body dynamics

TL;DR

This paper identifies a conserved quantity in the dynamics of thin bodies with metric symmetries, aiding in solving equilibrium configurations such as rotating, flowing strings, and extends classical concepts like Bernoulli's constant to these systems.

Contribution

It introduces a new conserved quantity specific to thin bodies with metric symmetries and demonstrates its application in analyzing equilibrium states of rotating, flowing strings.

Findings

Conserved quantity exists along the symmetry coordinate.

Application to rotating, flowing string equilibria.

Extension of Bernoulli's constant concept.

Abstract

Thin, solid bodies with metric symmetries admit a restricted form of reparameterization invariance. Their dynamical equilibria include motions with both rigid and flowing aspects. On such configurations, a quantity is conserved along the intrinsic coordinate corresponding to the symmetry. As an example of its utility, this conserved quantity is combined with linear and angular momentum currents to construct solutions for the equilibria of a rotating, flowing string, for which it is akin to Bernoulli's constant.